Related papers: Whitney's Theorem for oscillatiing on $R$ function…
This work presents two simple criteria for determining the oscillatory nature of solutions to second-order differential equations with deviated arguments. These criteria extend the (Leighton-Wintner)-type criteria established by G.Q. Wang…
The Riccati equation method is used to establish an oscillatory and a non oscillatory criteria for nonhomogeneous linear systems of two first-order ordinary differential equations. It is shown that the obtained oscillatory criterion is a…
The Riccati equation method is used to establish oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations.We show that the obtained oscillation criterion is a generalization of J. S.…
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
The famous Whitney formula relates the winding number of the smooth generic curve in the real plane to the number of its self-intersection points counted with appropriate signs. We extend this formula to smooth immersions of R^n to R^{2n}.…
The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain…
The Riccati equation method is used to establish some oscillatory criteria for the second order linear functional - differential equations of multiple terms with locally integrable coefficients. An interval oscillation criterion for the…
The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths on shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute…
Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory one…
We give explicit formulas for Whittaker functions for the class one principal series representations of the orthogonal groups $ SO_{2n+1}(\R) $ of odd degree. Our formulas are similar to the recursive formulas for Whittaker functions on…
We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.
The work of Adler provides necessary and sufficient conditions for the Wronskian of a given sequence of eigenfunctions of Schr\"odinger's equation to have constant sign in its domain of definition. We extend this result by giving explicit…
We propose the existence theorem for bounded solutions to the system of 2-nd order ODE. Dynamical applications have been considered.
The classical Whitney formula relates the number of times an oriented plane curve cuts itself to its rotation number and the index of a base point. In this paper we generalize Whitney's formula to curves on an oriented punctured surface. To…
Formulas for stable differentiation of piecewise-smooth functions are given. The data are noisy values of these functions. The locations of discontinuity points and the sizes of the jumps across these points are not assumed known, but found…
We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization…
The Riccati equation method is used to establish some new oscillatory criteria for the hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of coefficients of the hamiltonian system.…
The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions…
Local oscillation of a function satisfying a H\"older condition is considered and it is proved that its growth is governed by a version of the Law of the Iterated Logarithm.
The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of linear four dimensional hamiltonian systems. An oscillatory and two non oscillatory criteria are proved. On an example the obtained…